Finite Group Databasebeta

← #11781724

Subgroups — #11781724

Order 1152.

338 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593752C211yesmaximal, characteristic, complemented
2#10593418C211yesmaximal, characteristic, complemented
3#10590551C212yesmaximal, complemented
4#10590041C211yesmaximal, characteristic, complemented
5#10590037C212yesmaximal, complemented
6C2×#3788—21no—
7C2×#3774—21no—
8C2×#3774—21no—
9#64102C2211yescharacteristic
10#63914C2212yes—
11C2×#3714—22no—
12#63778—21no—
13C4⋊#622C2211yescharacteristic
14C4×#622C2211yescharacteristic
15C3×#809—22no—
16#63572C2212yes—
17#4786—62no—
18C2×C4⋊(C3⋊D3)D411yescharacteristic
19C2×C4×C3⋊D3—21no—
20C2×C3×D12—22no—
21C2×#625—22no—
22C2×#625—22no—
23C2×#622—21no—
24C2×#622D411yescharacteristic
25C2×#622D411yescharacteristic
26#3788—42no—
27#3774—42no—
28#3774—42no—
29C32×C4⋊C4D411yescharacteristic
30#3752—21no—
31C4×C3⋊Dic3C2311yescharacteristic
32C2×C3×C3⋊C8—22no—
33#3714—44no—
34#1687—91nomaximal, Sylow
35#940—62no—
36C2×#213—62no—
37C2×D24—62no—
38#893—62no—
39C3×#102—62no—
40Dic3⋊C8—62no—
41#809—22no—
42C22×C3⋊D3—21no—
43C22×C3×D3—42no—
44C2×C32×C4—21no—
45C2×C32×C4C2×D411yescharacteristic
46C2×C3⋊Dic3C2×D411yescharacteristic
47C2×C3⋊Dic3#4111yescharacteristic
48C4⋊(C3⋊D3)—22no—
49C4×C3⋊D3—41no—
50C4×C3⋊D3—41no—
51C3×D12—42no—
52C3×D12—42no—
53#625—42no—
54#625—42no—
55#625—82no—
56#622—21no—
57#622—41no—
58#622D812yescomplemented
59C3×C3⋊C8—42no—
60#493—91no—
61#459—92no—
62#436—91no—
63#334—91no—
64#331—92no—
65C2×C3×D4—62no—
66C2×#67—122no—
67C2×#67—122no—
68C2×D12—22no—
69C2×D12—62no—
70C2×C4×D3—122no—
71C2×C3×C8—62no—
72C3×C4⋊C4—22no—
73#213—124no—
74(C2×D3)⋊C4—122no—
75C4×Dic3—62no—
76C2×C3⋊C8—22no—
77D24—124no—
78C22×C32#12111yescharacteristic
79C2×C3⋊D3—41no—
80C2×C3⋊D3—41no—
81C2×C3⋊D3—41no—
82C2×C3×D3—82no—
83C2×C3×D3—82no—
84C2×C3×D3—82no—
85C32×C4—41no—
86C32×C4AGL(1,ℤ/8)12yes—
87C3⋊Dic3—21no—
88C3⋊Dic3C2×D811yescharacteristic
89C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
90C2×D8—182no—
91C2×D8—181no—
92C2×D8—181no—
93C2×M16—181no—
94#127—92no—
95C4×D4—91no—
96C4⋊C8—92no—
97C4⋊C8—91no—
98#102—62no—
99C22⋊C8—181no—
100C4×C8—91no—
101C23×C3—122no—
102C22×D3—42no—
103C22×D3—122no—
104C3×D4—122no—
105C3×D4—122no—
106C2×C3×C4—22no—
107C2×C3×C4—42no—
108#67—242no—
109#67—242no—
110#67—244no—
111C2×Dic3—62no—
112C2×Dic3—62no—
113D12—42no—
114D12—42no—
115D12—64no—
116D12—122no—
117C4×D3—242no—
118C4×D3—242no—
119C3×C8—122no—
120C3⋊C8—42no—
121C2×C32#45911yescharacteristic
122C2×C32#46911yescharacteristic
123C2×C32#47211yescharacteristic
124C3⋊D3—81no—
125C3×D3—162no—
126C2×D4—62no—
127C2×D4—91no—
128C2×D4—182no—
129C2×D4—182no—
130C22×C4—181no—
131D8—362no—
132D8—364no—
133D8—362no—
134M16—362no—
135C2×C8—62no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—181no—
139C4⋊C4GO+(4,𝔽2)11yescharacteristic
140C22⋊C4—181no—
141C42—91no—
142C22×C3—22no—
143C22×C3—242no—
144C22×C3—242no—
145C22×C3—242no—
146C2×D3—82no—
147C2×D3—82no—
148C2×D3—82no—
149C2×D3—124no—
150C2×D3—242no—
151C2×D3—242no—
152C3×C4—22no—
153C3×C4—22no—
154C3×C4—82no—
155Dic3—62no—
156Dic3—62no—
157Dic3—122no—
158C32#168711yescharacteristic, complemented, Sylow
159C23—122no—
160C23—181no—
161D4—122no—
162D4—122no—
163D4—182no—
164D4—362no—
165D4—362no—
166D4—722no—
167C2×C4—21no—
168C2×C4—91no—
169C2×C4—91no—
170C2×C4—361no—
171C2×C4—361no—
172C2×C4C2×GO+(4,𝔽2)11yescharacteristic
173C8—92no—
174C8—122no—
175C8—181no—
176C8—361no—
177C2×C3—22no—
178C2×C3—22no—
179C2×C3—22no—
180C2×C3—482no—
181D3—162no—
182D3—244no—
183C22—242no—
184C22—242no—
185C22—242no—
186C22—361no—
187C22—361no—
188C22—361no—
189C22#6424211yescharacteristic
190C4—41no—
191C4—91no—
192C4—91no—
193C4—181no—
194C4#6422412yes—
195C3—22no—
196C2—482no—
197C2—721no—
198C2#1059342911yescharacteristic
199C2#1059346411yescharacteristic
200C2#1059347911yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1687
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10593752C2semidirect
2. #10593418C2semidirect
3. #10590551C2semidirect
4. #10590041C2semidirect
5. #10590037C2semidirect
58. #622D8semidirect
158. C32#1687semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105937522
#105934182
#105905512
#105900412
#105900372
#16879